- 縦偏極パートン分布関数解析に対する、破砕関数の影響 - The Effect of Errors of Fragmentation Functions on the Analysis of Parton Helicity Distribution - 縦偏極パートン分布関数解析に対する、破砕関数の影響 - Tokyo Tech Y. Imazu, Y. Miyachi, T.-A. Shibata Mar. 25, 2007 Contents 1. Motivation 2. FF and pPDF Analyses 3. Effects of the error of FFs on pPDF analysis 4. Summary The subject of my master thesis is QCD analysis of parton helicity distributions with HERMES SIDIS data

1. Motivation

I estimated the errors of FFs based on Ktetzer parameterization Polarized Inclusive DIS : Polarized Semi-Inclusive DIS : SIDIS Asymmetry Fragmentation functions (FFs) are important elements in SIDIS asymmetry. Universality Fragmentation Functions (FFs) : ← determined by pQCD analysis of hadron productions in e+ e－ collision “ KKP ” : Nucl. Phys., B582, (2000) 514, “ Kretzer ” : Phys. Rev., D62, (2000) 054001 SIDIS is a DIS process with additional detection of the final state hadron. In my master course study, I did the global QCD analysis. In the analysis, I included pSIDIS data given by HERMES and SMC to separate quark – anti quark distribution effectively. In the calculation of pSIDIS asymmetry, fragmentation functions take part to express the hadron fragment process. By virtue of universality, we can use the FFs which are determined by pQCD analysis with e+ e- collision results to the SIDIS calculation. Many FFs are now given by many analysis groups. For the purpose of flavor separation with SIDIS data, I applied Kretzer FF to my analysis. But, because FFs are also determined by pQCD analysis, Kretzer FFs contain errors. What is still not clear is how much the error of FFs have an effect to the calculation of A1h. As the first step, we evaluated the errors of FFs and studied the effect of FF error on the A_1^h calc.. I estimated the errors of FFs based on Ktetzer parameterization How large is the effect? The error of FFs could affect the determination of ⊿q.

2. pPDF and FF Analyses Analysis including SIDIS data from SMC and HERMES - Brute force method for the convolution integrals in x and z. - Analysis with inclusive data converged and are consistent with other pPDF QCD analysis - LO analysis ( reported in Spring 2006 ) - NLO analysis was carried out. Error estimation of FF - Statistical error estimation for Kretzer-FF ( reported in Autumn 2006)

Semi-inclusive DIS NLO Experiment Theory : Error from fit (⊿χ2＝１) 0.1 0.01 Experiment Theory Semi-inclusive DIS : Error from fit (⊿χ2＝１)

Parton Helicity Distributions Results of NLO ⊿q analysis with SIDIS data with central values of my FFs ⊿u = 0.85±0.05 ⊿d = -0.41±0.13 ⊿sea = -0.07±0.04 ⊿g = 0.04±0.33 With the assumption of SU(3) symmetric sea, motivated by D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018 to obtain well-defined error bands; well converged covariant matrix

Hadron Production in e+ e- collision NLO SLAC-TPC SLAC-SLD SLAC-SLD_c SLAC-SLD_b EX. h = Experiment Theory フィットがうまく言ってる。Fitted curve both in LO and NLO. Z 0.1 1 Z

Fragmentation Functions EX. Results of the analysis of NLO pion FF with Kretzer parameterization up → π + gluon → π +

3. Effects of the errors of FFs on pPDF analysis

・Comparison of σA_FF with experimental errors (bar) and pPDF induced errors (band) ( AExp – AThe ) / σA_FF @ NLO (σA_FF : From Pion FF ) : Error from pPDF fit

・The effect of FF on @ NLO pPDF: Fixed K+ π+ π+ K+

4. Summary ・Semi-Inclusive DIS, which needs information on FF, is an important process to obtain information on flavor decomposition. ・pPDF and FF analyses are in progress in pQCD numerical calc. framework. SIDIS Analysis at NLO Statistical error on Kretzer-type FF ・The effect of the error of FF on pPDF analysis was studied in several ways, based on my current results of pPDF and FF analyses. ・The effect tuned out to be small. Future Subjects: ・Rather strong dependence on the choice of FF models D. de Florian et al. (DNS05): Phys. Rev. D71, (2005) 094018 Investigation of new models of FF and its validity

・ Current chi-squared values of pPDF fit 278.0

3. Effects of the errors of FFs on pPDF analysis ・Estimation of σA_FF : A1h error from FFs pPDF: Fixed h = π+ proton target σA_FF = Few % @ LO Almost the same effect even @ NLO